Where to raise family in Queens?

So I grew up in Suffolk Long Island where you have to be driven everywhere. But currently live in the city(UWS right now). My family and I are at the stage where we want to find our forever home with a perfect balance between the two.

We’ve been looking at Holliswood, Jamaica Estates. So if you have details about these areas great, but we are also very open to other neighborhoods. We just want a house in queens with UWS vibes(community/familyfriendly), but traditional Long Island suburb feel(houses).

We want: -single family house 4 bedrooms($1-2million budget) -house must have yard/backyard space -parks nearby/greenery -easy commute to Suffolk and Manhattan -can walk to stores nearby easily -mixed community (preference towards chinese, black - we are interracial) -homeschooling community(co-ops) -good food options nearby